{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a32972f5",
   "metadata": {},
   "source": [
    "# The Extended Kalman Filter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "520a9d67",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c5102106",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <style>\n",
       "        .output_wrapper, .output {\n",
       "            height:auto !important;\n",
       "            max-height:100000px;\n",
       "        }\n",
       "        .output_scroll {\n",
       "            box-shadow:none !important;\n",
       "            webkit-box-shadow:none !important;\n",
       "        }\n",
       "        </style>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#format the book\n",
    "import book_format\n",
    "book_format.set_style()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c67ac590",
   "metadata": {},
   "source": [
    "请在继续之前安装 SymPy。 有关说明，请参阅第 0 章。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e369e68",
   "metadata": {},
   "source": [
    "我们已经开发了线性卡尔曼滤波器的理论。 然后，在最后两章中，我们讨论了使用卡尔曼滤波器解决非线性问题的话题。 在本章中，我们将学习扩展卡尔曼滤波器 (EKF)。 EKF 通过在当前估计点线性化系统来处理非线性，然后使用线性卡尔曼滤波器对这个线性化系统进行滤波。 它是最早用于非线性问题的技术之一，并且仍然是最常用的技术。\n",
    "\n",
    "EKF 给滤波器设计者带来了重大的数学挑战； 这是本书最具挑战性的章节。 我尽我所能避免使用 EKF，转而采用其他已开发的技术来过滤非线性问题。 然而，这个话题是不可避免的； 该领域的所有经典论文和大多数当前论文都使用 EKF。 即使您在自己的工作中不使用 EKF，您也需要熟悉该主题才能阅读文献。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3d58654",
   "metadata": {},
   "source": [
    "## Linearizing the Kalman Filter\n",
    "\n",
    "卡尔曼滤波器使用线性方程，因此它不适用于非线性问题。 问题在两个方面可能是非线性的。 首先，过程模型可能是非线性的。 穿过大气层的物体会遇到阻力，这会降低其加速度。 阻力系数根据物体的速度而变化。 由此产生的行为是非线性的 - 它不能用线性方程建模。 其次，测量可能是非线性的。 例如，雷达为目标提供距离和方位。 我们使用非线性三角函数来计算目标的位置。\n",
    "\n",
    "对于线性滤波器，我们有这些过程和测量模型的方程:\n",
    "\n",
    "$$\\begin{aligned}\\dot{\\mathbf x} &= \\mathbf{Ax} + w_x\\\\\n",
    "\\mathbf z &= \\mathbf{Hx} + w_z\n",
    "\\end{aligned}$$\n",
    "\n",
    "其中 $\\mathbf A$ 是系统动态矩阵。 使用**卡尔曼滤波器数学**一章中介绍的状态空间方法，这些方程可以转换为\n",
    "\n",
    "$$\\begin{aligned}\\bar{\\mathbf x} &= \\mathbf{Fx} \\\\\n",
    "\\mathbf z &= \\mathbf{Hx}\n",
    "\\end{aligned}$$\n",
    "\n",
    "其中 $\\mathbf F$ 是*基本矩阵*。 噪声 $w_x$ 和 $w_z$ 项被合并到矩阵 $\\mathbf R$ 和 $\\mathbf Q$ 中。 这种形式的方程允许我们计算步骤 $k$ 的状态，给定步骤 $k$ 的测量值和步骤 $k-1$ 的状态估计值。 在前面的章节中，我通过使用牛顿方程描述的问题来建立你的直觉并最小化数学。 我们知道如何根据高中物理设计 $\\mathbf F$\n",
    "\n",
    "对于非线性模型，线性表达式 $\\mathbf{Fx} + \\mathbf{Bu}$ 被非线性函数 $f(\\mathbf x, \\mathbf u)$ 代替，线性表达式 $\\mathbf{Hx}$ 由非线性函数 $h(\\mathbf x)$ 代替：\n",
    "\n",
    "$$\\begin{aligned}\\dot{\\mathbf x} &= f(\\mathbf x, \\mathbf u) + w_x\\\\\n",
    "\\mathbf z &= h(\\mathbf x) + w_z\n",
    "\\end{aligned}$$\n",
    "\n",
    "您可能会想象我们可以通过找到一组新的卡尔曼滤波器方程来优化求解这些方程。 但是，如果您还记得 **非线性过滤** 章节中的图表，您就会记得通过非线性函数传递高斯分布会导致概率分布不再是高斯分布。 所以这是行不通的。\n",
    "\n",
    "EKF 不会改变卡尔曼滤波器的线性方程。 相反，它*线性化*当前估计点的非线性方程，并在线性卡尔曼滤波器中使用这种线性化。\n",
    "\n",
    "*线性化*意味着它听起来像什么。 我们找到一条与定义点处的曲线最匹配的线。 下图将抛物线 $f(x)=x^2-2x$ 在 $x=1.5$ 处线性化。*Linearize* 表示它的意思。 我们找到一条与定义点处的曲线最匹配的线。 下图将抛物线 $f(x)=x^2-2x$ 线性化为 $x=1.5$。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1effc04e",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import kf_book.ekf_internal as ekf_internal\n",
    "ekf_internal.show_linearization()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3dfdf11d",
   "metadata": {},
   "source": [
    "如果上面的曲线是过程模型，那么虚线显示了该曲线的线性化估计值 $x=1.5$。\n",
    "\n",
    "我们通过求导数来线性化系统，求出曲线的斜率：\n",
    "\n",
    "$$\\begin{aligned}\n",
    "f(x) &= x^2 -2x \\\\\n",
    "\\frac{df}{dx} &= 2x - 2\n",
    "\\end{aligned}$$\n",
    "\n",
    "然后在 $x$ 处评估它：\n",
    "\n",
    "$$\\begin{aligned}m &= f'(x=1.5) \\\\&= 2(1.5) - 2 \\\\&= 1\\end{aligned}$$ \n",
    "\n",
    "线性化微分方程组是类似的。 我们线性化 $f(\\mathbf x, \\mathbf u)$ 和 $h(\\mathbf x)$ x_t$ 和 $\\mathbf u_t$。 我们称矩阵的偏导数为 [*Jacobian*](https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant)。 这给了我们离散状态转移矩阵和测量模型矩阵：\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathbf F \n",
    "&= {\\frac{\\partial{f(\\mathbf x_t, \\mathbf u_t)}}{\\partial{\\mathbf x}}}\\biggr|_{{\\mathbf x_t},{\\mathbf u_t}} \\\\\n",
    "\\mathbf H &= \\frac{\\partial{h(\\bar{\\mathbf x}_t)}}{\\partial{\\bar{\\mathbf x}}}\\biggr|_{\\bar{\\mathbf x}_t} \n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "这导致 EKF 的以下等式。 我在与线性过滤器的差异周围放了框：\n",
    "\n",
    "$$\\begin{array}{l|l}\n",
    "\\text{linear Kalman filter} & \\text{EKF} \\\\\n",
    "\\hline \n",
    "& \\boxed{\\mathbf F = {\\frac{\\partial{f(\\mathbf x_t, \\mathbf u_t)}}{\\partial{\\mathbf x}}}\\biggr|_{{\\mathbf x_t},{\\mathbf u_t}}} \\\\\n",
    "\\mathbf{\\bar x} = \\mathbf{Fx} + \\mathbf{Bu} & \\boxed{\\mathbf{\\bar x} = f(\\mathbf x, \\mathbf u)}  \\\\\n",
    "\\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf{T}+\\mathbf Q  & \\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf{T}+\\mathbf Q \\\\\n",
    "\\hline\n",
    "& \\boxed{\\mathbf H = \\frac{\\partial{h(\\bar{\\mathbf x}_t)}}{\\partial{\\bar{\\mathbf x}}}\\biggr|_{\\bar{\\mathbf x}_t}} \\\\\n",
    "\\textbf{y} = \\mathbf z - \\mathbf{H \\bar{x}} & \\textbf{y} = \\mathbf z - \\boxed{h(\\bar{x})}\\\\\n",
    "\\mathbf{K} = \\mathbf{\\bar{P}H}^\\mathsf{T} (\\mathbf{H\\bar{P}H}^\\mathsf{T} + \\mathbf R)^{-1} & \\mathbf{K} = \\mathbf{\\bar{P}H}^\\mathsf{T} (\\mathbf{H\\bar{P}H}^\\mathsf{T} + \\mathbf R)^{-1} \\\\\n",
    "\\mathbf x=\\mathbf{\\bar{x}} +\\mathbf{K\\textbf{y}} & \\mathbf x=\\mathbf{\\bar{x}} +\\mathbf{K\\textbf{y}} \\\\\n",
    "\\mathbf P= (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar{P}} & \\mathbf P= (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar{P}}\n",
    "\\end{array}$$\n",
    "\n",
    "我们通常不使用 $\\mathbf{Fx}$ 来传播 EKF 的状态，因为线性化会导致不准确。 通常使用合适的数值积分技术（例如 Euler 或 Runge Kutta）计算 $\\bar{\\mathbf x}$。 因此我写了 $\\mathbf{\\bar x} = f(\\mathbf x, \\mathbf u)$。 出于同样的原因，我们在残差计算中不使用 $\\mathbf{H\\bar{x}}$，而是选择更准确的 $h(\\bar{\\mathbf x})$。\n",
    "\n",
    "我认为理解 EKF 的最简单方法是从一个例子开始。 稍后您可能想回来重新阅读本节。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "025981d5",
   "metadata": {},
   "source": [
    "## Example: Tracking a Airplane\n",
    "\n",
    "本示例使用地基雷达跟踪飞机。 我们在上一章中为这个问题实现了一个 UKF。 现在我们将针对同一问题实施 EKF，以便我们可以比较滤波器性能和实施滤波器所需的工作水平。\n",
    "\n",
    "雷达通过发射一束无线电波并扫描返回反弹来工作。 光束路径中的任何东西都会将一些信号反射回雷达。 通过对反射信号返回雷达所需的时间进行计时，系统可以计算*斜距* - 从雷达装置到物体的直线距离。\n",
    "\n",
    "雷达斜距$r$和仰角$\\epsilon$与飞机水平位置$x$和高度$y$的关系如下图所示："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c1acb882",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ekf_internal.show_radar_chart()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b852df4b",
   "metadata": {},
   "source": [
    "这给了我们等式：\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\epsilon &= \\tan^{-1} \\frac y x\\\\\n",
    "r^2 &= x^2 + y^2\n",
    "\\end{aligned}$$ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6cf6aa8",
   "metadata": {},
   "source": [
    "### Design the State Variables\n",
    "\n",
    "我们想在假设速度和高度恒定的情况下跟踪飞机的位置，并测量到飞机的斜距。 这意味着我们需要 3 个状态变量——水平距离、水平速度和高度：\n",
    "\n",
    "$$\\mathbf x = \\begin{bmatrix}\\mathtt{distance} \\\\\\mathtt{velocity}\\\\ \\mathtt{altitude}\\end{bmatrix}=    \\begin{bmatrix}x \\\\ \\dot x\\\\ y\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "862f398d",
   "metadata": {},
   "source": [
    "### Design the Process Model\n",
    "\n",
    "我们假设飞机采用牛顿运动学系统。 我们在前面的章节中使用过这个模型，所以通过检查你可能会认识到我们想要\n",
    "\n",
    "$$\\mathbf F = \\left[\\begin{array}{cc|c} 1 & \\Delta t & 0\\\\\n",
    "0 & 1 & 0 \\\\ \\hline\n",
    "0 & 0 & 1\\end{array}\\right]$$\n",
    "\n",
    "我已将矩阵分成块以显示左上块是 $x$ 的恒定速度模型，右下块是 $y$ 的恒定位置模型。\n",
    "\n",
    "但是，让我们练习查找这些矩阵。 我们用一组微分方程对系统进行建模。 我们需要一个形式为\n",
    "\n",
    "$$\\dot{\\mathbf x} = \\mathbf{Ax} + \\mathbf{w}$$\n",
    "\n",
    "其中 $\\mathbf{w}$ 是系统噪声。\n",
    "\n",
    "变量 $x$ 和 $y$ 是独立的，因此我们可以分别计算它们。 一维运动的微分方程为：\n",
    "\n",
    "$$\\begin{aligned}v &= \\dot x \\\\\n",
    "a &= \\ddot{x} = 0\\end{aligned}$$\n",
    "\n",
    "现在我们把微分方程变成状态空间形式。 如果这是一个二阶或更高阶微分系统，我们必须首先将它们简化为一组等效的一阶方程。 方程是一阶的，所以我们把它们放在状态空间矩阵的形式中\n",
    "\n",
    "$$\\begin{aligned}\\begin{bmatrix}\\dot x \\\\ \\ddot{x}\\end{bmatrix} &= \\begin{bmatrix}0&1\\\\0&0\\end{bmatrix} \\begin{bmatrix}x \\\\ \n",
    "\\dot x\\end{bmatrix} \\\\ \\dot{\\mathbf x} &= \\mathbf{Ax}\\end{aligned}$$\n",
    "\n",
    "其中 $\\mathbf A=\\begin{bmatrix}0&1\\\\0&0\\end{bmatrix}$.\n",
    "\n",
    "回想一下 $\\mathbf A$ 是*系统动力学矩阵*。 它描述了一组线性微分方程。 我们必须从中计算状态转移矩阵 $\\mathbf F$。 $\\mathbf F$ 描述了一组离散的线性方程，这些方程为离散时间步 $\\Delta t$ 计算 $\\mathbf x$。\n",
    "\n",
    "计算 $\\mathbf F$ 的常用方法是使用矩阵指数的幂级数展开：\n",
    "\n",
    "$$\\mathbf F(\\Delta t) = e^{\\mathbf A\\Delta t} = \\mathbf{I} + \\mathbf A\\Delta t  + \\frac{(\\mathbf A\\Delta t)^2}{2!} + \\frac{(\\mathbf A \\Delta t)^3}{3!} + ... $$\n",
    "\n",
    "$\\mathbf A^2 = \\begin{bmatrix}0&0\\\\0&0\\end{bmatrix}$，所以$\\mathbf A$ 的所有高次幂也是$\\mathbf{0}$。 因此幂级数展开是：\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathbf F &=\\mathbf{I} + \\mathbf At + \\mathbf{0} \\\\\n",
    "&= \\begin{bmatrix}1&0\\\\0&1\\end{bmatrix} + \\begin{bmatrix}0&1\\\\0&0\\end{bmatrix}\\Delta t\\\\\n",
    "\\mathbf F &= \\begin{bmatrix}1&\\Delta t\\\\0&1\\end{bmatrix}\n",
    "\\end{aligned}$$\n",
    "\n",
    "这与运动学方程使用的结果相同！ 除了说明从线性微分方程找到状态转移矩阵之外，这个练习是不必要的。 我们将用一个需要使用这种技术的例子来结束本章。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c38c121",
   "metadata": {},
   "source": [
    "### Design the Measurement Model\n",
    "\n",
    "测量函数采用先验 $\\bar{\\mathbf x}$ 的状态估计并将其转换为斜距距离的测量值。 我们使用勾股定理推导出：\n",
    "\n",
    "$$h(\\bar{\\mathbf x}) = \\sqrt{x^2 + y^2}$$\n",
    "\n",
    "由于平方根，斜距与地面位置之间的关系是非线性的。 我们通过评估其在 $\\mathbf x_t$ 处的偏导数对其进行线性化：\n",
    "\n",
    "$$\n",
    "\\mathbf H = \\frac{\\partial{h(\\bar{\\mathbf x})}}{\\partial{\\bar{\\mathbf x}}}\\biggr|_{\\bar{\\mathbf x}_t}\n",
    "$$\n",
    "\n",
    "\n",
    "矩阵的偏导数称为雅可比矩阵，其形式为\n",
    "\n",
    "$$\\frac{\\partial \\mathbf H}{\\partial \\bar{\\mathbf x}} = \n",
    "\\begin{bmatrix}\n",
    "\\frac{\\partial h_1}{\\partial x_1} & \\frac{\\partial h_1}{\\partial x_2} &\\dots \\\\\n",
    "\\frac{\\partial h_2}{\\partial x_1} & \\frac{\\partial h_2}{\\partial x_2} &\\dots \\\\\n",
    "\\vdots & \\vdots\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "换句话说，矩阵中的每个元素都是函数 $h$ 相对于 $x$ 变量的偏导数。 对于我们的问题，我们有\n",
    "\n",
    "$$\\mathbf H = \\begin{bmatrix}{\\partial h}/{\\partial x} & {\\partial h}/{\\partial \\dot{x}} & {\\partial h}/{\\partial y}\\end{bmatrix}$$\n",
    "\n",
    "Solving each in turn:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial h}{\\partial x} &= \\frac{\\partial}{\\partial x} \\sqrt{x^2 + y^2} \\\\\n",
    "&= \\frac{x}{\\sqrt{x^2 + y^2}}\n",
    "\\end{aligned}$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial h}{\\partial \\dot{x}} &=\n",
    "\\frac{\\partial}{\\partial \\dot{x}} \\sqrt{x^2 + y^2} \\\\ \n",
    "&= 0\n",
    "\\end{aligned}$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\frac{\\partial h}{\\partial y} &= \\frac{\\partial}{\\partial y} \\sqrt{x^2 + y^2} \\\\ \n",
    "&= \\frac{y}{\\sqrt{x^2 + y^2}}\n",
    "\\end{aligned}$$\n",
    "\n",
    "giving us \n",
    "\n",
    "$$\\mathbf H = \n",
    "\\begin{bmatrix}\n",
    "\\frac{x}{\\sqrt{x^2 + y^2}} & \n",
    "0 &\n",
    "&\n",
    "\\frac{y}{\\sqrt{x^2 + y^2}}\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "这可能看起来令人生畏，所以退后一步并认识到所有这些数学都是在做一些非常简单的事情。 我们有一个非线性的飞机斜距方程。 卡尔曼滤波器只适用于线性方程，因此我们需要找到一个近似于 $\\mathbf H$ 的线性方程。 正如我们上面讨论的，在给定点找到非线性方程的斜率是一个很好的近似。 对于卡尔曼滤波器，“给定点”是状态变量 $\\mathbf x$，因此我们需要取相对于 $\\mathbf x$ 的斜距的导数。 对于线性卡尔曼滤波器，$\\mathbf H$ 是我们在运行滤波器之前计算的常数。 对于 EKF，$\\mathbf H$ 在每一步都会随着评估点 $\\bar{\\mathbf x}$ 在每个时期的变化而更新。\n",
    "\n",
    "为了更具体地说明这一点，现在让我们编写一个 Python 函数来计算这个问题的 $h$ 的雅可比行列式。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6df56413",
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "def HJacobian_at(x):\n",
    "    \"\"\" compute Jacobian of H matrix at x \"\"\"\n",
    "\n",
    "    horiz_dist = x[0]\n",
    "    altitude   = x[2]\n",
    "    denom = sqrt(horiz_dist**2 + altitude**2)\n",
    "    return array ([[horiz_dist/denom, 0., altitude/denom]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "611fc24f",
   "metadata": {},
   "source": [
    "最后，让我们提供 $h(\\bar{\\mathbf x})$ 的代码："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ac08df1f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def hx(x):\n",
    "    \"\"\" compute measurement for slant range that\n",
    "    would correspond to state x.\n",
    "    \"\"\"\n",
    "    \n",
    "    return (x[0]**2 + x[2]**2) ** 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d9096bb",
   "metadata": {},
   "source": [
    "现在让我们为我们的雷达编写一个模拟。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a0c656e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.random import randn\n",
    "import math\n",
    "\n",
    "class RadarSim:\n",
    "    \"\"\" Simulates the radar signal returns from an object\n",
    "    flying at a constant altityude and velocity in 1D. \n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, dt, pos, vel, alt):\n",
    "        self.pos = pos\n",
    "        self.vel = vel\n",
    "        self.alt = alt\n",
    "        self.dt = dt\n",
    "        \n",
    "    def get_range(self):\n",
    "        \"\"\" Returns slant range to the object. Call once \n",
    "        for each new measurement at dt time from last call.\n",
    "        \"\"\"\n",
    "        \n",
    "        # add some process noise to the system\n",
    "        self.vel = self.vel  + .1*randn()\n",
    "        self.alt = self.alt + .1*randn()\n",
    "        self.pos = self.pos + self.vel*self.dt\n",
    "    \n",
    "        # add measurement noise\n",
    "        err = self.pos * 0.05*randn()\n",
    "        slant_dist = math.sqrt(self.pos**2 + self.alt**2)\n",
    "        \n",
    "        return slant_dist + err"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8dc316f8",
   "metadata": {},
   "source": [
    "### Design Process and Measurement Noise\n",
    "\n",
    "雷达测量到目标的距离。 我们将使用 $\\sigma_{range}= 5$ 米作为噪声。 这给了我们\n",
    "\n",
    "$$\\mathbf R = \\begin{bmatrix}\\sigma_{range}^2\\end{bmatrix} = \\begin{bmatrix}25\\end{bmatrix}$$\n",
    "\n",
    "$\\mathbf Q$ 的设计需要一些讨论。 状态 $\\mathbf x= \\begin{bmatrix}x & \\dot x & y\\end{bmatrix}^\\mathtt{T}$。 前两个元素是位置（向下距离）和速度，因此我们可以使用“Q_discrete_white_noise”噪声来计算 $\\mathbf Q$ 左上角的值。 $\\mathbf x$ 的第三个元素是高度，我们假设它与下行距离无关。 这导致我们对 $\\mathbf Q$ 的块设计：\n",
    "\n",
    "$$\\mathbf Q = \\begin{bmatrix}\\mathbf Q_\\mathtt{x} & 0 \\\\ 0 & \\mathbf Q_\\mathtt{y}\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ceeee9c3",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "`FilterPy` 提供了类 `ExtendedKalmanFilter`。 它的工作原理与我们一直在使用的 `KalmanFilter` 类类似，不同之处在于它允许您提供一个函数来计算 $\\mathbf H$ 和函数 $h(\\mathbf x)$ 的雅可比行列式。\n",
    "\n",
    "我们首先导入过滤器并创建它。 `x` 的维度是 3，`z` 的维度是 1。\n",
    "\n",
    "```python\n",
    "从 filterpy.kalman 导入 ExtendedKalmanFilter\n",
    "\n",
    "rk = ExtendedKalmanFilter(dim_x=3, dim_z=1)\n",
    "\n",
    "我们创建雷达模拟器：\n",
    "\n",
    "```python\n",
    "radar = RadarSim(dt, pos=0., vel=100., alt=1000.)\n",
    "\n",
    "我们将在飞机实际位置附近初始化过滤器：\n",
    "\n",
    "```python\n",
    "rk.x = array([radar.pos, radar.vel-10, radar.alt+100])\n",
    "```\n",
    "\n",
    "我们使用上面计算的泰勒级数展开式的第一项分配系统矩阵：\n",
    "\n",
    "```python\n",
    "dt = 0.05\n",
    "rk.F = eye(3) + array([[0, 1, 0],\n",
    "                       [0, 0, 0],\n",
    "                       [0, 0, 0]])*dt\n",
    "```\n",
    "\n",
    "在为 $\\mathbf R$、$\\mathbf Q$ 和 $\\mathbf P$ 分配合理的值后，我们可以通过一个简单的循环运行过滤器。 我们将计算 $\\mathbf H$ 和 $h(x)$ 的雅可比矩阵的函数传递给 `update` 方法。\n",
    "\n",
    "```python\n",
    "for i in range(int(20/dt)):\n",
    "    z = radar.get_range()\n",
    "    rk.update(array([z]), HJacobian_at, hx)\n",
    "    rk.predict()\n",
    "```\n",
    "\n",
    "添加一些样板代码来保存和绘制我们得到的结果："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c9d73397",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from filterpy.common import Q_discrete_white_noise\n",
    "from filterpy.kalman import ExtendedKalmanFilter\n",
    "from numpy import eye, array, asarray\n",
    "import numpy as np\n",
    "\n",
    "dt = 0.05\n",
    "rk = ExtendedKalmanFilter(dim_x=3, dim_z=1)\n",
    "radar = RadarSim(dt, pos=0., vel=100., alt=1000.)\n",
    "\n",
    "# make an imperfect starting guess\n",
    "rk.x = array([radar.pos-100, radar.vel+100, radar.alt+1000])\n",
    "\n",
    "rk.F = eye(3) + array([[0, 1, 0],\n",
    "                       [0, 0, 0],\n",
    "                       [0, 0, 0]]) * dt\n",
    "\n",
    "range_std = 5. # meters\n",
    "rk.R = np.diag([range_std**2])\n",
    "rk.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n",
    "rk.Q[2,2] = 0.1\n",
    "rk.P *= 50\n",
    "\n",
    "xs, track = [], []\n",
    "for i in range(int(20/dt)):\n",
    "    z = radar.get_range()\n",
    "    track.append((radar.pos, radar.vel, radar.alt))\n",
    "    \n",
    "    rk.update(array([z]), HJacobian_at, hx)\n",
    "    xs.append(rk.x)\n",
    "    rk.predict()\n",
    "\n",
    "xs = asarray(xs)\n",
    "track = asarray(track)\n",
    "time = np.arange(0, len(xs)*dt, dt)\n",
    "ekf_internal.plot_radar(xs, track, time)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11eb600c",
   "metadata": {},
   "source": [
    "根据您使用导数的经验，您可能会发现计算雅可比矩阵很困难。 即使你觉得它很容易，稍微困难一点的问题也很容易导致非常困难的计算。\n",
    "\n",
    "如附录 A 中所述，我们可以使用 SymPy 包为我们计算雅可比行列式。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "75e65018",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}x\\\\x_{vel}\\\\y\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡ x  ⎤\n",
       "⎢    ⎥\n",
       "⎢xᵥₑₗ⎥\n",
       "⎢    ⎥\n",
       "⎣ y  ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{x}{\\sqrt{x^{2} + y^{2}}} & 0 & \\frac{y}{\\sqrt{x^{2} + y^{2}}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡     x                y      ⎤\n",
       "⎢────────────  0  ────────────⎥\n",
       "⎢   _________        _________⎥\n",
       "⎢  ╱  2    2        ╱  2    2 ⎥\n",
       "⎣╲╱  x  + y       ╲╱  x  + y  ⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import sympy\n",
    "from IPython.display import display\n",
    "sympy.init_printing(use_latex='mathjax')\n",
    "\n",
    "x, x_vel, y = sympy.symbols('x, x_vel y')\n",
    "\n",
    "H = sympy.Matrix([sympy.sqrt(x**2 + y**2)])\n",
    "\n",
    "state = sympy.Matrix([x, x_vel, y])\n",
    "J = H.jacobian(state)\n",
    "\n",
    "display(state)\n",
    "display(J)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27b4b3e8",
   "metadata": {},
   "source": [
    "这个结果与我们上面计算的结果相同，而且我们的努力要少得多！"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fce03a26",
   "metadata": {},
   "source": [
    "## Robot Localization\n",
    "\n",
    "是时候尝试解决真正的问题了。 我警告你这部分很难。 然而，大多数书籍选择简单的、具有简单答案的教科书式问题，你会想知道如何解决现实世界的问题。\n",
    "\n",
    "我们将考虑机器人定位问题。 我们已经在 **Unscented Kalman Filter** 章节中实现了这一点，如果您还没有阅读，我建议您现在阅读。 在这个场景中，我们有一个机器人在景观中移动，使用传感器检测地标。 这可能是一辆使用计算机视觉识别树木、建筑物和其他地标的自动驾驶汽车。 它可能是为您的房子吸尘的小型机器人之一，或者是仓库中的机器人。\n",
    "\n",
    "该机器人有 4 个轮子，与汽车使用的配置相同。 它通过转动前轮来操纵。 这会导致机器人在向前移动时围绕后轴枢转。 这是我们必须建模的非线性行为。\n",
    "\n",
    "过程模型和测量模型都是非线性的。 EKF 兼顾了两者，因此我们暂时得出结论，EKF 是解决此问题的可行选择。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e56b7398",
   "metadata": {},
   "source": [
    "### Robot Motion Model\n",
    "\n",
    "在第一次近似时，汽车通过在向前移动的同时转动前轮来实现转向。 汽车的前部沿车轮所指的方向移动，同时围绕后轮胎转动。 这个简单的描述因摩擦引起的打滑、橡胶轮胎在不同速度下的不同行为以及外胎需要与内胎行驶不同的半径等问题而变得复杂。 精确建模转向需要一组复杂的微分方程。\n",
    "\n",
    "对于低速机器人应用，已发现更简单的*自行车模型* 表现良好。 这是模型的描述："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e842b89c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ekf_internal.plot_bicycle()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f69de8f8",
   "metadata": {},
   "source": [
    "在 **Unscented Kalman Filter** 章节中，我们推导出了这些方程：\n",
    "\n",
    "$$\\begin{aligned} \n",
    "\\beta &= \\frac d w \\tan(\\alpha) \\\\\n",
    "x &= x - R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
    "y &= y + R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
    "\\theta &= \\theta + \\beta\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "其中 $\\theta$ 是机器人的航向。\n",
    "\n",
    "如果您对转向模型不感兴趣，则无需详细了解该模型。 需要认识到的重要一点是我们的运动模型是非线性的，我们需要使用卡尔曼滤波器来处理它。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63cd8444",
   "metadata": {},
   "source": [
    "### Design the State Variables\n",
    "\n",
    "对于我们的过滤器，我们将保持机器人的位置 $x,y$ 和方向 $\\theta$：\n",
    "\n",
    "$$\\mathbf x = \\begin{bmatrix}x \\\\ y \\\\ \\theta\\end{bmatrix}$$\n",
    "\n",
    "我们的控制输入 $\\mathbf u$ 是速度 $v$ 和转向角 $\\alpha$：\n",
    "\n",
    "$$\\mathbf u = \\begin{bmatrix}v \\\\ \\alpha\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "806ec290",
   "metadata": {},
   "source": [
    "### Design the System Model\n",
    "\n",
    "我们将系统建模为非线性运动模型加上噪声。\n",
    "\n",
    "$$\\bar x = f(x, u) + \\mathcal{N}(0, Q)$$\n",
    "\n",
    "使用我们在上面创建的机器人的运动模型，我们可以将其扩展为\n",
    "\n",
    "$$\\bar{\\begin{bmatrix}x\\\\y\\\\\\theta\\end{bmatrix}} = \\begin{bmatrix}x\\\\y\\\\\\theta\\end{bmatrix} + \n",
    "\\begin{bmatrix}- R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
    "R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
    "\\beta\\end{bmatrix}$$\n",
    "\n",
    "我们通过取 $f(x,u)$ 的雅可比行列式来找到 $\\mathbf F$。\n",
    "\n",
    "$$\\mathbf F = \\frac{\\partial f(x, u)}{\\partial x} =\\begin{bmatrix}\n",
    "\\frac{\\partial f_1}{\\partial x} & \n",
    "\\frac{\\partial f_1}{\\partial y} &\n",
    "\\frac{\\partial f_1}{\\partial \\theta}\\\\\n",
    "\\frac{\\partial f_2}{\\partial x} & \n",
    "\\frac{\\partial f_2}{\\partial y} &\n",
    "\\frac{\\partial f_2}{\\partial \\theta} \\\\\n",
    "\\frac{\\partial f_3}{\\partial x} & \n",
    "\\frac{\\partial f_3}{\\partial y} &\n",
    "\\frac{\\partial f_3}{\\partial \\theta}\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "当我们计算这些时，我们得到\n",
    "\n",
    "$$\\mathbf F = \\begin{bmatrix}\n",
    "1 & 0 & -R\\cos(\\theta) + R\\cos(\\theta+\\beta) \\\\\n",
    "0 & 1 & -R\\sin(\\theta) + R\\sin(\\theta+\\beta) \\\\\n",
    "0 & 0 & 1\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "我们可以用 SymPy 仔细检查我们的工作。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5fb66a91",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0 & - \\frac{w \\cos{\\left(\\theta \\right)}}{\\tan{\\left(\\alpha \\right)}} + \\frac{w \\cos{\\left(\\frac{t v \\tan{\\left(\\alpha \\right)}}{w} + \\theta \\right)}}{\\tan{\\left(\\alpha \\right)}}\\\\0 & 1 & - \\frac{w \\sin{\\left(\\theta \\right)}}{\\tan{\\left(\\alpha \\right)}} + \\frac{w \\sin{\\left(\\frac{t v \\tan{\\left(\\alpha \\right)}}{w} + \\theta \\right)}}{\\tan{\\left(\\alpha \\right)}}\\\\0 & 0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                        ⎛t⋅v⋅tan(α)    ⎞⎤\n",
       "⎢                   w⋅cos⎜────────── + θ⎟⎥\n",
       "⎢        w⋅cos(θ)        ⎝    w         ⎠⎥\n",
       "⎢1  0  - ──────── + ─────────────────────⎥\n",
       "⎢         tan(α)            tan(α)       ⎥\n",
       "⎢                                        ⎥\n",
       "⎢                        ⎛t⋅v⋅tan(α)    ⎞⎥\n",
       "⎢                   w⋅sin⎜────────── + θ⎟⎥\n",
       "⎢        w⋅sin(θ)        ⎝    w         ⎠⎥\n",
       "⎢0  1  - ──────── + ─────────────────────⎥\n",
       "⎢         tan(α)            tan(α)       ⎥\n",
       "⎢                                        ⎥\n",
       "⎣0  0                  1                 ⎦"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sympy\n",
    "from sympy.abc import alpha, x, y, v, w, R, theta\n",
    "from sympy import symbols, Matrix\n",
    "sympy.init_printing(use_latex=\"mathjax\", fontsize='16pt')\n",
    "time = symbols('t')\n",
    "d = v*time\n",
    "beta = (d/w)*sympy.tan(alpha)\n",
    "r = w/sympy.tan(alpha)\n",
    "\n",
    "fxu = Matrix([[x-r*sympy.sin(theta) + r*sympy.sin(theta+beta)],\n",
    "              [y+r*sympy.cos(theta)- r*sympy.cos(theta+beta)],\n",
    "              [theta+beta]])\n",
    "F = fxu.jacobian(Matrix([x, y, theta]))\n",
    "F"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56c3480d",
   "metadata": {},
   "source": [
    "那看起来有点复杂。 我们可以使用 SymPy 来替换术语："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "30a8780e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0 & - R \\cos{\\left(\\theta \\right)} + R \\cos{\\left(\\beta + \\theta \\right)}\\\\0 & 1 & - R \\sin{\\left(\\theta \\right)} + R \\sin{\\left(\\beta + \\theta \\right)}\\\\0 & 0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1  0  -R⋅cos(θ) + R⋅cos(β + θ)⎤\n",
       "⎢                              ⎥\n",
       "⎢0  1  -R⋅sin(θ) + R⋅sin(β + θ)⎥\n",
       "⎢                              ⎥\n",
       "⎣0  0             1            ⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# reduce common expressions\n",
    "B, R = symbols('beta, R')\n",
    "F = F.subs((d/w)*sympy.tan(alpha), B)\n",
    "F.subs(w/sympy.tan(alpha), R)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89319f88",
   "metadata": {},
   "source": [
    "这种形式验证了雅可比矩阵的计算是正确的。\n",
    "\n",
    "现在我们可以将注意力转向噪音。 在这里，噪声在我们的控制输入中，所以它在*控制空间*中。 换句话说，我们命令特定的速度和转向角，但我们需要将其转换为 $x、y、\\theta$ 中的误差。 在实际系统中，这可能会因速度而异，因此每次预测都需要重新计算。 我会选择这个作为噪声模型； 对于真正的机器人，您需要选择一个能够准确描述系统错误的模型。\n",
    "\n",
    "$$\\mathbf{M} = \\begin{bmatrix}\\sigma_{vel}^2 & 0 \\\\ 0 & \\sigma_\\alpha^2\\end{bmatrix}$$\n",
    "\n",
    "如果这是一个线性问题，我们将使用现在熟悉的 $\\mathbf{FMF}^\\mathsf T$ 形式从控制空间转换到状态空间。 由于我们的运动模型是非线性的，我们不会试图找到一个封闭形式的解决方案，而是用我们将命名为 $\\mathbf{V}$ 的雅可比行列式对其进行线性化。\n",
    "\n",
    "$$\\mathbf{V} = \\frac{\\partial f(x, u)}{\\partial u} \\begin{bmatrix}\n",
    "\\frac{\\partial f_1}{\\partial v} & \\frac{\\partial f_1}{\\partial \\alpha} \\\\\n",
    "\\frac{\\partial f_2}{\\partial v} & \\frac{\\partial f_2}{\\partial \\alpha} \\\\\n",
    "\\frac{\\partial f_3}{\\partial v} & \\frac{\\partial f_3}{\\partial \\alpha}\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "这些偏导数变得非常难以处理。 让我们用 SymPy 计算它们。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "22f9e5c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}t \\cos{\\left(\\beta + \\theta \\right)} & \\frac{d \\left(\\tan^{2}{\\left(\\alpha \\right)} + 1\\right) \\cos{\\left(\\beta + \\theta \\right)}}{\\tan{\\left(\\alpha \\right)}} - \\frac{w \\left(- \\tan^{2}{\\left(\\alpha \\right)} - 1\\right) \\sin{\\left(\\theta \\right)}}{\\tan^{2}{\\left(\\alpha \\right)}} + \\frac{w \\left(- \\tan^{2}{\\left(\\alpha \\right)} - 1\\right) \\sin{\\left(\\beta + \\theta \\right)}}{\\tan^{2}{\\left(\\alpha \\right)}}\\\\t \\sin{\\left(\\beta + \\theta \\right)} & \\frac{d \\left(\\tan^{2}{\\left(\\alpha \\right)} + 1\\right) \\sin{\\left(\\beta + \\theta \\right)}}{\\tan{\\left(\\alpha \\right)}} + \\frac{w \\left(- \\tan^{2}{\\left(\\alpha \\right)} - 1\\right) \\cos{\\left(\\theta \\right)}}{\\tan^{2}{\\left(\\alpha \\right)}} - \\frac{w \\left(- \\tan^{2}{\\left(\\alpha \\right)} - 1\\right) \\cos{\\left(\\beta + \\theta \\right)}}{\\tan^{2}{\\left(\\alpha \\right)}}\\\\\\frac{t}{R} & \\frac{d \\left(\\tan^{2}{\\left(\\alpha \\right)} + 1\\right)}{w}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡                ⎛   2       ⎞                ⎛     2       ⎞            ⎛     2       ⎞           ⎤\n",
       "⎢              d⋅⎝tan (α) + 1⎠⋅cos(β + θ)   w⋅⎝- tan (α) - 1⎠⋅sin(θ)   w⋅⎝- tan (α) - 1⎠⋅sin(β + θ)⎥\n",
       "⎢t⋅cos(β + θ)  ────────────────────────── - ──────────────────────── + ────────────────────────────⎥\n",
       "⎢                        tan(α)                        2                            2              ⎥\n",
       "⎢                                                   tan (α)                      tan (α)           ⎥\n",
       "⎢                                                                                                  ⎥\n",
       "⎢                ⎛   2       ⎞                ⎛     2       ⎞            ⎛     2       ⎞           ⎥\n",
       "⎢              d⋅⎝tan (α) + 1⎠⋅sin(β + θ)   w⋅⎝- tan (α) - 1⎠⋅cos(θ)   w⋅⎝- tan (α) - 1⎠⋅cos(β + θ)⎥\n",
       "⎢t⋅sin(β + θ)  ────────────────────────── + ──────────────────────── - ────────────────────────────⎥\n",
       "⎢                        tan(α)                        2                            2              ⎥\n",
       "⎢                                                   tan (α)                      tan (α)           ⎥\n",
       "⎢                                                                                                  ⎥\n",
       "⎢                                                  ⎛   2       ⎞                                   ⎥\n",
       "⎢     t                                          d⋅⎝tan (α) + 1⎠                                   ⎥\n",
       "⎢     ─                                          ───────────────                                   ⎥\n",
       "⎣     R                                                 w                                          ⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V = fxu.jacobian(Matrix([v, alpha]))\n",
    "V = V.subs(sympy.tan(alpha)/w, 1/R) \n",
    "V = V.subs(time*v/R, B)\n",
    "V = V.subs(time*v, 'd')\n",
    "V"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b04ec77",
   "metadata": {},
   "source": [
    "这应该让您了解 EKF 在数学上变得难以处理的速度有多快。\n",
    "\n",
    "这为我们提供了预测方程的最终形式：\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathbf{\\bar x} &= \\mathbf x + \n",
    "\\begin{bmatrix}- R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n",
    "R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n",
    "\\beta\\end{bmatrix}\\\\\n",
    "\\mathbf{\\bar P} &=\\mathbf{FPF}^{\\mathsf T} + \\mathbf{VMV}^{\\mathsf T}\n",
    "\\end{aligned}$$\n",
    "\n",
    "\n",
    "这种线性化形式并不是预测 $\\mathbf x$ 的唯一方法。 例如，我们可以使用*Runge Kutta* 等数值积分技术来计算运动\n",
    "的机器人。 如果时间步长相对较大，这将是必需的。 使用 EKF 不像使用卡尔曼滤波器那样切割和干燥。 对于实际问题，您必须用微分方程仔细建模系统，然后确定解决该系统的最合适方法。 正确的方法取决于您需要的精度、方程的非线性程度、您的处理器预算以及数值稳定性问题。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72163eb6",
   "metadata": {},
   "source": [
    "### Design the Measurement Model\n",
    "\n",
    "机器人的传感器为景观中的多个已知位置提供嘈杂的方位和距离测量。 测量模型必须将状态 $\\begin{bmatrix}x & y&\\theta\\end{bmatrix}^\\mathsf T$ 转换为一个范围并指向地标。 如果 $\\mathbf p$\n",
    "是地标的位置，范围 $r$ 是\n",
    "\n",
    "$$r = \\sqrt{(p_x - x)^2 + (p_y - y)^2}$$\n",
    "\n",
    "传感器提供相对于机器人方向的方位，因此我们必须从方位中减去机器人的方位以获得传感器读数，如下所示：\n",
    "\n",
    "$$\\phi = \\arctan(\\frac{p_y - y}{p_x - x}) - \\theta$$\n",
    "\n",
    "因此我们的测量模型 $h$ 是\n",
    "\n",
    "$$\\begin{aligned}\n",
    "\\mathbf z& = h(\\bar{\\mathbf x}, \\mathbf p) &+ \\mathcal{N}(0, R)\\\\\n",
    "&= \\begin{bmatrix}\n",
    "\\sqrt{(p_x - x)^2 + (p_y - y)^2} \\\\\n",
    "\\arctan(\\frac{p_y - y}{p_x - x}) - \\theta \n",
    "\\end{bmatrix} &+ \\mathcal{N}(0, R)\n",
    "\\end{aligned}$$\n",
    "\n",
    "这显然是非线性的，所以我们需要在 $\\mathbf x$ 处取其雅可比行列式对 $h$ 进行线性化。 我们用下面的 SymPy 计算它。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f39b5889",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{- p_{x} + x}{\\sqrt{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}}} & \\frac{- p_{y} + y}{\\sqrt{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}}} & 0\\\\- \\frac{- p_{y} + y}{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}} & - \\frac{p_{x} - x}{\\left(p_{x} - x\\right)^{2} + \\left(p_{y} - y\\right)^{2}} & -1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡          -pₓ + x                      -p_y + y             ⎤\n",
       "⎢───────────────────────────  ───────────────────────────  0 ⎥\n",
       "⎢   ________________________     ________________________    ⎥\n",
       "⎢  ╱         2            2     ╱         2            2     ⎥\n",
       "⎢╲╱  (pₓ - x)  + (p_y - y)    ╲╱  (pₓ - x)  + (p_y - y)      ⎥\n",
       "⎢                                                            ⎥\n",
       "⎢       -(-p_y + y)                   -(pₓ - x)              ⎥\n",
       "⎢  ──────────────────────       ──────────────────────     -1⎥\n",
       "⎢          2            2               2            2       ⎥\n",
       "⎣  (pₓ - x)  + (p_y - y)        (pₓ - x)  + (p_y - y)        ⎦"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "px, py = symbols('p_x, p_y')\n",
    "z = Matrix([[sympy.sqrt((px-x)**2 + (py-y)**2)],\n",
    "            [sympy.atan2(py-y, px-x) - theta]])\n",
    "z.jacobian(Matrix([x, y, theta]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ebe3685",
   "metadata": {},
   "source": [
    "现在我们需要把它写成一个 Python 函数。 例如我们可能会写："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "715b434c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "\n",
    "def H_of(x, landmark_pos):\n",
    "    \"\"\" compute Jacobian of H matrix where h(x) computes \n",
    "    the range and bearing to a landmark for state x \"\"\"\n",
    "\n",
    "    px = landmark_pos[0]\n",
    "    py = landmark_pos[1]\n",
    "    hyp = (px - x[0, 0])**2 + (py - x[1, 0])**2\n",
    "    dist = sqrt(hyp)\n",
    "\n",
    "    H = array(\n",
    "        [[-(px - x[0, 0]) / dist, -(py - x[1, 0]) / dist, 0],\n",
    "         [ (py - x[1, 0]) / hyp,  -(px - x[0, 0]) / hyp, -1]])\n",
    "    return H"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ef63696",
   "metadata": {},
   "source": [
    "我们还需要定义一个将系统状态转换为度量的函数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9596010b",
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import atan2\n",
    "\n",
    "def Hx(x, landmark_pos):\n",
    "    \"\"\" takes a state variable and returns the measurement\n",
    "    that would correspond to that state.\n",
    "    \"\"\"\n",
    "    px = landmark_pos[0]\n",
    "    py = landmark_pos[1]\n",
    "    dist = sqrt((px - x[0, 0])**2 + (py - x[1, 0])**2)\n",
    "\n",
    "    Hx = array([[dist],\n",
    "                [atan2(py - x[1, 0], px - x[0, 0]) - x[2, 0]]])\n",
    "    return Hx"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a86ad5ea",
   "metadata": {},
   "source": [
    "### Design Measurement Noise\n",
    "\n",
    "可以合理地假设距离和方位测量的噪声是独立的，因此\n",
    "\n",
    "$$\\mathbf R=\\begin{bmatrix}\\sigma_{range}^2 & 0 \\\\ 0 & \\sigma_{bearing}^2\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19774f05",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "我们将使用`FilterPy` 的`ExtendedKalmanFilter` 类来实现过滤器。 它的“predict()”方法使用过程模型的标准线性方程。 我们是非线性的，所以我们必须用我们自己的实现覆盖`predict()`。 我还想使用这个类来模拟机器人，所以我将添加一个方法 `move()` 来计算机器人的位置，`predict()` 和我的模拟都可以调用。\n",
    "\n",
    "预测步骤的矩阵非常大。 在编写这段代码时，我在最终让它工作之前犯了几个错误。 我只是通过使用 SymPy 的 `evalf` 函数发现了我的错误。 `evalf` 使用变量的特定值评估 SymPy `Matrix`。 我决定向您演示这种技术，并在卡尔曼滤波器代码中使用了 `evalf`。 您需要了解几点。\n",
    "\n",
    "首先，`evalf` 使用字典来指定值。 例如，如果你的矩阵包含一个 `x` 和 `y`，你可以写\n",
    "\n",
    "```python\n",
    "    M.evalf(subs={x:3, y:17})\n",
    "```\n",
    "\n",
    "评估“x=3”和“y=17”的矩阵。\n",
    "\n",
    "其次，`evalf` 返回一个 `sympy.Matrix` 对象。 使用 `numpy.array(M).astype(float)` 将其转换为 NumPy 数组。 `numpy.array(M)` 创建一个类型为 `object` 的数组，这不是你想要的。\n",
    "\n",
    "这是EKF的代码："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "263c0732",
   "metadata": {},
   "outputs": [],
   "source": [
    "from filterpy.kalman import ExtendedKalmanFilter as EKF\n",
    "from numpy import array, sqrt\n",
    "class RobotEKF(EKF):\n",
    "    def __init__(self, dt, wheelbase, std_vel, std_steer):\n",
    "        EKF.__init__(self, 3, 2, 2)\n",
    "        self.dt = dt\n",
    "        self.wheelbase = wheelbase\n",
    "        self.std_vel = std_vel\n",
    "        self.std_steer = std_steer\n",
    "\n",
    "        a, x, y, v, w, theta, time = symbols(\n",
    "            'a, x, y, v, w, theta, t')\n",
    "        d = v*time\n",
    "        beta = (d/w)*sympy.tan(a)\n",
    "        r = w/sympy.tan(a)\n",
    "    \n",
    "        self.fxu = Matrix(\n",
    "            [[x-r*sympy.sin(theta)+r*sympy.sin(theta+beta)],\n",
    "             [y+r*sympy.cos(theta)-r*sympy.cos(theta+beta)],\n",
    "             [theta+beta]])\n",
    "\n",
    "        self.F_j = self.fxu.jacobian(Matrix([x, y, theta]))\n",
    "        self.V_j = self.fxu.jacobian(Matrix([v, a]))\n",
    "\n",
    "        # save dictionary and it's variables for later use\n",
    "        self.subs = {x: 0, y: 0, v:0, a:0, \n",
    "                     time:dt, w:wheelbase, theta:0}\n",
    "        self.x_x, self.x_y, = x, y \n",
    "        self.v, self.a, self.theta = v, a, theta\n",
    "\n",
    "    def predict(self, u):\n",
    "        self.x = self.move(self.x, u, self.dt)\n",
    "\n",
    "        self.subs[self.theta] = self.x[2, 0]\n",
    "        self.subs[self.v] = u[0]\n",
    "        self.subs[self.a] = u[1]\n",
    "\n",
    "        F = array(self.F_j.evalf(subs=self.subs)).astype(float)\n",
    "        V = array(self.V_j.evalf(subs=self.subs)).astype(float)\n",
    "\n",
    "        # covariance of motion noise in control space\n",
    "        M = array([[self.std_vel*u[0]**2, 0], \n",
    "                   [0, self.std_steer**2]])\n",
    "\n",
    "        self.P = F @ self.P @ F.T + V @ M @ V.T\n",
    "\n",
    "    def move(self, x, u, dt):\n",
    "        hdg = x[2, 0]\n",
    "        vel = u[0]\n",
    "        steering_angle = u[1]\n",
    "        dist = vel * dt\n",
    "\n",
    "        if abs(steering_angle) > 0.001: # is robot turning?\n",
    "            beta = (dist / self.wheelbase) * tan(steering_angle)\n",
    "            r = self.wheelbase / tan(steering_angle) # radius\n",
    "\n",
    "            dx = np.array([[-r*sin(hdg) + r*sin(hdg + beta)], \n",
    "                           [r*cos(hdg) - r*cos(hdg + beta)], \n",
    "                           [beta]])\n",
    "        else: # moving in straight line\n",
    "            dx = np.array([[dist*cos(hdg)], \n",
    "                           [dist*sin(hdg)], \n",
    "                           [0]])\n",
    "        return x + dx"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c967ba59",
   "metadata": {},
   "source": [
    "现在我们有另一个问题要处理。 残差理论上计算为 $y = z - h(x)$ 但这不起作用，因为我们的测量包含一个角度。 假设 z 的方位角为 $1^\\circ$，而 $h(x)$ 的方位角为 $359^\\circ$。 天真地减去它们会产生 $-358^\\circ$ 的角度差，而正确的值是 $2^\\circ$。 我们必须编写代码来正确计算轴承残差。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "6dcb8f2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def residual(a, b):\n",
    "    \"\"\" compute residual (a-b) between measurements containing \n",
    "    [range, bearing]. Bearing is normalized to [-pi, pi)\"\"\"\n",
    "    y = a - b\n",
    "    y[1] = y[1] % (2 * np.pi)    # force in range [0, 2 pi)\n",
    "    if y[1] > np.pi:             # move to [-pi, pi)\n",
    "        y[1] -= 2 * np.pi\n",
    "    return y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d246e52",
   "metadata": {},
   "source": [
    "其余代码运行模拟并绘制结果，现在不需要太多注释。 我创建了一个包含地标坐标的变量“地标”。 我每秒更新模拟机器人位置 10 次，但每秒只运行一次 EKF。 这是出于两个原因。 首先，我们没有使用 Runge Kutta 来对微分运动方程进行积分，因此较窄的时间步长可以让我们的模拟更加准确。 其次，在嵌入式系统中，处理速度有限是很正常的。 这迫使您仅在绝对需要时才运行卡尔曼滤波器。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "f9188556",
   "metadata": {},
   "outputs": [],
   "source": [
    "from filterpy.stats import plot_covariance_ellipse\n",
    "from math import sqrt, tan, cos, sin, atan2\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "dt = 1.0\n",
    "\n",
    "def z_landmark(lmark, sim_pos, std_rng, std_brg):\n",
    "    x, y = sim_pos[0, 0], sim_pos[1, 0]\n",
    "    d = np.sqrt((lmark[0] - x)**2 + (lmark[1] - y)**2)  \n",
    "    a = atan2(lmark[1] - y, lmark[0] - x) - sim_pos[2, 0]\n",
    "    z = np.array([[d + randn()*std_rng],\n",
    "                  [a + randn()*std_brg]])\n",
    "    return z\n",
    "\n",
    "def ekf_update(ekf, z, landmark):\n",
    "    ekf.update(z, HJacobian=H_of, Hx=Hx, \n",
    "               residual=residual,\n",
    "               args=(landmark), hx_args=(landmark))\n",
    "    \n",
    "                \n",
    "def run_localization(landmarks, std_vel, std_steer, \n",
    "                     std_range, std_bearing,\n",
    "                     step=10, ellipse_step=20, ylim=None):\n",
    "    ekf = RobotEKF(dt, wheelbase=0.5, std_vel=std_vel, \n",
    "                   std_steer=std_steer)\n",
    "    ekf.x = array([[2, 6, .3]]).T # x, y, steer angle\n",
    "    ekf.P = np.diag([.1, .1, .1])\n",
    "    ekf.R = np.diag([std_range**2, std_bearing**2])\n",
    "\n",
    "    sim_pos = ekf.x.copy() # simulated position\n",
    "    # steering command (vel, steering angle radians)\n",
    "    u = array([1.1, .01]) \n",
    "\n",
    "    plt.figure()\n",
    "    plt.scatter(landmarks[:, 0], landmarks[:, 1],\n",
    "                marker='s', s=60)\n",
    "    \n",
    "    track = []\n",
    "    for i in range(200):\n",
    "        sim_pos = ekf.move(sim_pos, u, dt/10.) # simulate robot\n",
    "        track.append(sim_pos)\n",
    "\n",
    "        if i % step == 0:\n",
    "            ekf.predict(u=u)\n",
    "\n",
    "            if i % ellipse_step == 0:\n",
    "                plot_covariance_ellipse(\n",
    "                    (ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2], \n",
    "                     std=6, facecolor='k', alpha=0.3)\n",
    "\n",
    "            x, y = sim_pos[0, 0], sim_pos[1, 0]\n",
    "            for lmark in landmarks:\n",
    "                z = z_landmark(lmark, sim_pos,\n",
    "                               std_range, std_bearing)\n",
    "                ekf_update(ekf, z, lmark)\n",
    "\n",
    "            if i % ellipse_step == 0:\n",
    "                plot_covariance_ellipse(\n",
    "                    (ekf.x[0,0], ekf.x[1,0]), ekf.P[0:2, 0:2],\n",
    "                    std=6, facecolor='g', alpha=0.8)\n",
    "    track = np.array(track)\n",
    "    plt.plot(track[:, 0], track[:,1], color='k', lw=2)\n",
    "    plt.axis('equal')\n",
    "    plt.title(\"EKF Robot localization\")\n",
    "    if ylim is not None: plt.ylim(*ylim)\n",
    "    plt.show()\n",
    "    return ekf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "262ee443",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.024 0.042 0.002]\n"
     ]
    }
   ],
   "source": [
    "landmarks = array([[5, 10], [10, 5], [15, 15]])\n",
    "\n",
    "ekf = run_localization(\n",
    "    landmarks, std_vel=0.1, std_steer=np.radians(1),\n",
    "    std_range=0.3, std_bearing=0.1)\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2475cd17",
   "metadata": {},
   "source": [
    "我已将地标绘制为实心方块。 机器人的路径用黑线绘制。 预测步骤的协方差椭圆为浅灰色，更新的协方差以绿色显示。 为了使它们在这个比例下可见，我将椭圆边界设置为 6$\\sigma$。\n",
    "\n",
    "我们可以看到我们的运动模型增加了很多不确定性，并且大部分误差都在运动方向上。 我们根据蓝色椭圆的形状来确定。 经过几个步骤后，我们可以看到滤波器结合了地标测量，并且误差得到了改善。\n",
    "\n",
    "我在 UKF 章节中使用了相同的初始条件和标志性位置。 UKF 在误差椭圆方面取得了更好的精度。 就他们对 $\\mathbf x$ 的估计而言，两者的表现大致一样。\n",
    "\n",
    "现在让我们添加另一个地标。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "f275cc35",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.021 0.02  0.002]\n"
     ]
    }
   ],
   "source": [
    "landmarks = array([[5, 10], [10, 5], [15, 15], [20, 5]])\n",
    "\n",
    "ekf = run_localization(\n",
    "    landmarks, std_vel=0.1, std_steer=np.radians(1),\n",
    "    std_range=0.3, std_bearing=0.1)\n",
    "plt.show()\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e200d388",
   "metadata": {},
   "source": [
    "接近轨道末端的估计的不确定性较小。 通过仅使用前两个地标，我们可以看到多个地标对我们的不确定性的影响。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "f8758ddf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.021 0.045 0.   ]\n"
     ]
    }
   ],
   "source": [
    "ekf = run_localization(\n",
    "    landmarks[0:2], std_vel=1.e-10, std_steer=1.e-10,\n",
    "    std_range=1.4, std_bearing=.05)\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50ccc24d",
   "metadata": {},
   "source": [
    "在经过地标后，估计值会迅速偏离机器人的路径。 协方差也快速增长。 让我们看看只有一个地标会发生什么："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "59887d2b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.242 0.852 0.004]\n"
     ]
    }
   ],
   "source": [
    "ekf = run_localization(\n",
    "    landmarks[0:1], std_vel=1.e-10, std_steer=1.e-10,\n",
    "    std_range=1.4, std_bearing=.05)\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eada8de8",
   "metadata": {},
   "source": [
    "正如您可能怀疑的那样，一个地标会产生非常糟糕的结果。 相反，大量的地标使我们能够做出非常准确的估计。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "10220232",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final P: [0.008 0.009 0.001]\n"
     ]
    }
   ],
   "source": [
    "landmarks = array([[5, 10], [10,  5], [15, 15], [20,  5], [15, 10], \n",
    "                   [10,14], [23, 14], [25, 20], [10, 20]])\n",
    "\n",
    "ekf = run_localization(\n",
    "    landmarks, std_vel=0.1, std_steer=np.radians(1),\n",
    "    std_range=0.3, std_bearing=0.1, ylim=(0, 21))\n",
    "print('Final P:', ekf.P.diagonal())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f742c81",
   "metadata": {},
   "source": [
    "### Discussion\n",
    "\n",
    "我说这是一个真正的问题，在某些方面确实如此。我见过使用机器人运动模型的替代演示文稿，这些模型导致更简单的雅可比行列式。另一方面，我的运动模型在几个方面也很简单。首先，它使用自行车模型。一辆真正的汽车有两组轮胎，每组轮胎的行驶半径不同。轮子不能完美地抓住表面。我还假设机器人会立即响应控制输入。 Sebastian Thrun 在 *Probabilistic Robots* 中写道，这种简化的模型是合理的，因为过滤器在用于跟踪真实车辆时表现良好。这里的教训是，虽然您必须拥有一个相当准确的非线性模型，但它并不需要完美才能运行良好。作为设计师，您需要在模型的保真度、数学难度和执行线性代数所需的 CPU 时间之间取得平衡。\n",
    "\n",
    "这个问题的另一种简单化方式是我们假设我们知道地标和测量值之间的对应关系。但是假设我们正在使用雷达 - 我们如何知道特定信号返回对应于本地场景中的特定建筑物？这个问题暗示了 SLAM 算法 - 同时定位和映射。 SLAM 不是本书的重点，所以我不会详细说明这个话题。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "901217e6",
   "metadata": {},
   "source": [
    "## UKF vs EKF\n",
    "\n",
    "上一章我用UKF解决了这个问题。实现上的区别应该是很明显的。尽管有一个基本的运动模型，但计算状态和测量模型的雅可比行列式并不是微不足道的。一个不同的问题可能会导致雅可比矩阵很难或不可能通过分析推导出来。相比之下，UKF 只要求您提供一个计算系统运动模型的函数和另一个用于测量模型的函数。\n",
    "\n",
    "在很多情况下无法通过分析找到雅可比行列式。细节超出了本书的范围，但你必须使用数值方法来计算雅可比矩阵。这项工作并非微不足道，您将在 STEM 学校的硕士学位中花费很大一部分时间来学习技术来处理这种情况。即便如此，您可能也只能解决与您的领域相关的问题 - 航空工程师对 Navier Stokes 方程了解很多，但对化学反应速率建模了解不多。\n",
    "\n",
    "因此，UKF 很容易。它们准确吗？在实践中，它们的性能通常优于 EKF。您可以找到大量研究论文，证明 UKF 在各种问题领域都优于 EKF。不难理解为什么这是真的。 EKF 通过在单个点线性化系统模型和测量模型来工作，UKF 使用 $2n+1$ 点。\n",
    "\n",
    "我们来看一个具体的例子。取 $f(x) = x^3$ 并通过它传递高斯分布。我将使用蒙特卡罗模拟计算准确答案。我根据高斯分布随机生成 50,000 个点，每个点通过 $f(x)$，然后计算结果的均值和方差。\n",
    "\n",
    "EKF 通过求导数来找到评估点 $x$ 处的斜率来线性化函数。这个斜率成为我们用来变换高斯的线性函数。这是一个情节。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "8c081ee9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "actual mean=1.30, std=1.12\n",
      "EKF    mean=1.00, std=0.95\n"
     ]
    }
   ],
   "source": [
    "import kf_book.nonlinear_plots as nonlinear_plots\n",
    "nonlinear_plots.plot_ekf_vs_mc()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95249e82",
   "metadata": {},
   "source": [
    "EKF 计算相当不准确。 相比之下，这是 UKF 的表现："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "d5838cbf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "actual mean=1.30, std=1.13\n",
      "UKF    mean=1.30, std=1.08\n"
     ]
    }
   ],
   "source": [
    "nonlinear_plots.plot_ukf_vs_mc(alpha=0.001, beta=3., kappa=1.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abf3d9db",
   "metadata": {},
   "source": [
    "在这里我们可以看到，UKF 均值的计算精确到小数点后两位。 标准偏差略有偏差，但您也可以使用 $\\alpha$、$\\beta$ 和 $\\gamma$ 参数来微调 UKF 计算分布的方式，以生成 sigma 点。 这里我使用了 $\\alpha=0.001$、$\\beta=3$ 和 $\\gamma=1$。 随意修改它们以查看结果。 你应该能够得到比我更好的结果。 但是，避免为特定测试过度调整 UKF。 对于您的测试用例，它可能表现得更好，但总体而言更糟。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "60d35944",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
